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Why the Arts and Mathematics?

If you asked elementary teachers what they found beautiful in mathematics, would they be able to:

describe a beautiful mathematical idea?

tell an engaging story about a mathematics concept?

relay a surprise or wonder at the way a problem could be solved in many ways?

If you asked elementary students how they knew they were in math class, would they describe:

the excitement of learning new concepts?

how they solve problems in novel and creative ways?

how they all work together to cooperatively learn new concepts?

how mathematics is linked and related to so many things around them?

Chances are that the answer to at least some of these questions is, unfortunately, “No.” Mathematicians describe the math that they do as beautiful, or the work they do as collaborative. (Gadanidis, n.d.) This is not necessarily true when you talk to teachers and students in elementary school. Mathematics is sometimes seen as something you do, not something you create. It is set apart from other subjects, and its curriculum is further fragmentized into seemingly unrelated strands. Add to this, textbooks designed to cover curriculum expectations, and meet standards in a measurable way on standardized tests that can draw us away from a place where beauty, collaboration, and surprise are the norm rather than the exception. (Gadanidis & Hughes, 2011)

A paper that I wrote for a masters course on why and how we should embrace learning mathematics through the arts is available here.

The desire to create mathematics; to have a set of mathematical learning experiences that reflect real math; to have complex, rich problems that reveal beauty at the same time as mathematical concepts has driven the creation of the math and art books shared here. These books take the students through all five strands of the grade 7/8 Ontario Mathematics Curriculum all through the lens of the arts.

This work is provided to you with a Creative Commons Share Alike licence. Feel free to share, use, adapt, modify any or all of these math resources. The only caveat is that any derivative works must be shared freely with everyone as well.

Fibonacci

Patterning, ratio, rate, integers, fractions. All of these are covered through looking at the intricacies of the Fibonacci sequence. A math and arts investigation with choices organized around Howard Gardner’s multiple intelligences concludes the booklet. Available as a free epub on the the Apple iBooks store with embedded video. PDF version free to download from this link.

Giacometti

Ratio and proportion learned through looking for the golden ratio within the measurements of our bodies. Scale is explored through the the creation of wireframe scale sculptures of ourselves that echo Giacometti’s greatest sculptures. Available as a free epub on the the Apple iBooks store with embedded video. PDF version free to download from this link.

Mondrian

Area,proportion and ratio are investigated through learning about the abstract art of this great, iconic artist. The concluding task involves creating a work of art that uses the golden ratio to reveal mathematical understanding. Available as a free epub on the the Apple iBooks store with embedded video. PDF version free to download from this link.

Inquiry

Inquiry in mathematics . . . and the arts . . . with suggested topics that encapsulate the learning of the three previous booklets . . . all following Howard Gardner’s multiple intelligences. Available as a free epub on the the Apple iBooks store. PDF version free to download from this link.

Data visualization is a new field. It is a new way of helping people to look at data in novel ways which reveal new truths. After covering all the graphing skills necessary for grades 7 & 8, the students dive into analysis, proportional displays of data, and per capita representations of data while also learning to estimate and calculate square roots, and figure out the areas of various shapes including the circle. Focussing on narrative, the students develop the skills and understanding necessary to revealing truth in data. PDF version free to download from this link.

No math book is complete, nor do they ever cover everything your students might need. These supplementary materials were developed by my teaching partner and me to meet the needs of our students. Extra problems, more practice, links to the Nelson math text for even more practice, and assessment materials can all be had here. Each extra activity is annotated with the purpose and reasons behind their creation. PDF version free to download from this link.

A teacher’s guide of sorts. Guidance, curriculum links, teaching strategies, and the changing role of the teacher are included. This is not the traditional teacher guide in that it will not prescribe how to teach the activities in the student books, but it will set you on the correct path to discover a different way of teaching. Each activity has its related curriculum link (for math) as well as assessment prompts. Available as a free epub on the the Apple iBooks store. PDF version free to download from this link.

I have created a guided exploration and data assignment using the Gapminder.org website. It covers a large amount of the analysis expectations in grades 7 & 8. It’s untested at this point. I’d love some feedback, if possible.